What's Happened to the Phillips Curve? Flint Brayton, John M. Roberts, and John C. Williams Division of Research and Statistics Federal Reserve Board Washington, D.C. 20551 September 1999 Abstract The simultaneous occurrence in the second half of the 1990s of low and falling price inflation and low unemployment appears to be at odds with the properties of a standard Phillips curve. We find this result in a model in which inflation depends on the unem- ployment rate, past inflation, and conventional measures of price supply shocks. We show that, in such a model, long lags of past inflation are preferred to short lags, and that with long lags, the NAIRU is estimated precisely but is unstable in the 1990s. Two alternative modifications to the standard Phillips curve restore stability. One replaces the unemployment rate with capacity utilization. Although this change leads to more accurate inflation predictions in the recent period, the predictive ability of the utiliza- tion rate is not superior to that of the unemployment rate for the 1955 to 1998 sample as a whole. The second, and preferred, modification augments the standard Phillips curve to include an “error-correction” mechanism involving the markup of prices over trend unit labor costs. With the markup relatively high through much of the 1990s, this channel is estimated to have held down inflation over this period, and thus provides an explanation of the recent low inflation. Keywords: Inflation, NAIRU, Phillips curve. The authors acknowledge the comments and assistance of Peter Tulip and the comments of Robert Gor- don and other participants at the 1999 NBER Summer Institute on Monetary Economics. Views presented are those of the authors and do not necessarily represent those of the Federal Reserve Board or its staff. 1 Introduction and Summary The rise and fall of inflation in the United States during the 1970s and 1980s provided a testing ground for the Phillips curve model of inflation dynamics. And, according to some observers (Fuhrer 1995, Gordon 1997), such models performed admirably well in tracking actual inflation, both within and out of sample. Based on this achievement, many became convinced of the usefulness of such models as tools in predicting inflation. Unfortunately, the main feature of empirical Phillips curve models, that is, that inflation rises when labor markets tighten, appears to be turned on its head during the economic expansion of the 1990s, when the unemployment rate fell below its long-run average of around 6 percent and then slid under 5 percent, while inflation fell. One objective of this paper is to ascertain whether the recent performance of infla- tion is surprising in a statistical sense within the context of a canonical Phillips curve in which price inflation depends on the unemployment rate, past price inflation, and standard measures of price supply shocks. To provide a graphical preview of our conclusion that a significant shift likely has taken place in such a baseline model, figure 1 shows forecast errors for our preferred CPI equation.1 The upper panel of the figure contains one-quarter- ahead forecast errors based on successive reestimates of the equation over samples whose starting point is held fixed at 1955:Q1 and whose ending point advances one quarter at a time. The forecasts make use of the actual values of explanatory variables.2 While no individual error this decade lies outside of the 95 percent confidence range, inflation has consistently fallen short of the model's predictions over the past five years. Given the run of negative prediction errors, multi-period forecast errors and their con- fidence bands provide a better graphical depiction of the probability of the equation's re- cent performance. The lower panel of the figure plots the sequence of four-quarter-ahead forecast errors. These errors are derived in a manner analogous to that used for the one- 1The inflation series is the the all-items CPI index, modified from 1967 to 1983 so that homeownership costs are on a rental-equivalent basis, and adjusted since 1995 to eliminate effects of methodological changes. The explanatory variables consist of twenty-four quarterly lags of past inflation; contemporaneous values of a demographically weighted unemployment rate and a composite measure of relative food and energy price movements; an intercept; and a variable for the 1970s wage-price controls. The structure of this equation is discussed in more detail below. 2The use of forecasts conditional on actual values of explanatory variables is appropriate because the is- sues being examined concern the structure of the Phillips curve itself. Errors in forecasting the unemployment rate, for example, are not germane because conceptually they are associated with the performance of other equations in a forecasting system. 1 CPI Inflation: Forecast Errors (observations dated by end of forecast interval) (actual less predicted, annual rate) 95% confidence range one-quarter-ahead forecast error 2 1 0 -1 Figure 1 2 -2 four-quarter-ahead forecast error 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 step-ahead errors, except that within each four-quarter forecast interval, the forecast is a dynamic simulation in which inflation lags are set equal to simulated values. The most recent four-quarter forecasts have overpredicted inflation by as much as 1.3 percentage points, well outside of the 95 percent confidence range, which encompasses forecast errors of up to 0.9 percentage points. A tendency to overpredict inflation starting in the middle of this decade characterizes baseline equations for all six measures of inflation we study. For all but one, the magnitude of the prediction errors is sufficient to reject the hypothesis of stability of the equation's intercept at a significance level of 10 percent or lower. In the framework of these equa- tions, instability of the intercept can be interpreted as instability of the NAIRU—that is, the rate of unemployment consistent with stable inflation (Non-Accelerating Inflation Rate of Unemployment). We also find a close association between the number of lags of inflation included in the baseline equations and whether or not evidence of significant structural change is found. Equations such as ours with long inflation lags (up to twenty-four quarters) are generally unstable while those with short lags are not. In essence, estimates of the NAIRU are much more precise in long-lag equations than in short-lag equations, and consequently the level of the unemployment rate over the past few years is well below the 95 percent NAIRU confidence range of long-lag equations but not that of short-lag equations. The relationship between inflation lag length and NAIRU precision has been docu- mented by Staiger, Stock, and Watson (1997a)—hereafter, SSW—but they emphasize the wide confidence intervals for the NAIRU found in short-lag equations on grounds that such lag lengths are optimal according to either standard hypothesis tests or the use of infor- mation criteria to select lag lengths. Our long-lag equations are the outcome of using an information criteria to choose simultaneously lag lengths and coefficient smoothing re- strictions. Permitting smoothing restrictions leads to equations that have much longer lags on past inflation than is the case when lag coefficients are unrestricted, but with only a few independently estimated parameters because the lag coefficients are restricted to lie on low-order polynomials. We show that these long-lag Phillips curves, in addition to yielding much more precise estimates of the NAIRU, have better out-of-sample forecasting proper- ties than do the short-lag ones. Monte Carlo evidence indicates that the procedure of jointly searching over lag lengths and smoothing restrictions is reasonably accurate at finding the 3 “correct” model, whether or not it contains smoothed inflation coefficients. Our baseline analysis provides support for the type of Phillips curve long favored by Robert Gordon who for many years has reported a specification with twenty-four quarterly lags of past inflation.3 The tendency of our baseline equations to significantly overpredict inflation since the mid-1990s, however, is an indication of structural change—perhaps a decline of the NAIRU—or of misspecification. Because the baseline equations contain the relative rates of import price inflation and food and energy price inflation, the statistical evidence also permits the conclusion that recent declines in the relative prices of these supply variables are not sufficient to account fully for the low rate of inflation. We investigate two possible explanations for the breakdown or near-breakdown of the standard Phillips curve. One is the possibility that the capacity utilization rate—which has been near its historical average during the past few years—is a better measure of macroe- conomic slack than the unemployment rate, in which case the recent behavior of inflation would not be that extraordinary. From a conceptual perspective, the unemployment rate might be preferred because of its broader sectoral coverage. But as it turns out, movements of the utilization and unemployment rates are sufficiently similar over the past forty or so years that the goodness of fit of equations based on one is quite similar to the fit of equa- tions based on the other. Nonetheless, we find that Phillips curve equations that include the unemployment rate fit somewhat better over the postwar years than do those using capacity utilization. The outcome is closer to a toss up in out-of-sample forecasts, however. All told, the evidence does not provide strong support for the use of capacity utilization but neither does it suggest that the utilization rate is dominated by the unemployment rate. Our preferred explanation is based on an augmented Phillips curve that includes the level of the markup of price relative to trend unit labor costs as an error correction term.